Answer:
12 students
Step-by-step explanation:
Given
Required
Determine the number of students that eat lunch once a week
In Sets;
If out of 9, at least 7 eats one a week then
9 - 7 eats lunch once a week
<em>In other words;</em>
2 out of 9 students eat lunch once a week
Number of students in this category is then calculated as thus;
The answer is 28. My answer is correct. 7, 14& 21 can't be the LCM son the answer should be 28.
The answer is 60 because 10 x 2 is 20 and 5 x 8 is 40 and add those together to get 60
Answer:
y(t) = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t) + 1
Step-by-step explanation:
y" + y' + y = 1
This is a second order nonhomogenous differential equation with constant coefficients.
First, find the roots of the complementary solution.
y" + y' + y = 0
r² + r + 1 = 0
r = [ -1 ± √(1² − 4(1)(1)) ] / 2(1)
r = [ -1 ± √(1 − 4) ] / 2
r = -1/2 ± i√3/2
These roots are complex, so the complementary solution is:
y = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t)
Next, assume the particular solution has the form of the right hand side of the differential equation. In this case, a constant.
y = c
Plug this into the differential equation and use undetermined coefficients to solve:
y" + y' + y = 1
0 + 0 + c = 1
c = 1
So the total solution is:
y(t) = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t) + 1
To solve for c₁ and c₂, you need to be given initial conditions.
Answer:
flour per cup of sugar=2 1/2 cups of flour
sugar per cup of flour=2/5 cups of sugar
Step-by-step explanation:
